Spectral clustering steered low-rank representation for subspace segmentation

Wei, Lai; Yin, Jun; Wu, Aihua

doi:10.1016/j.jvcir.2016.03.017

Cited by 16 publications

(21 citation statements)

References 41 publications

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“…• We find a close relation between R-LRR (Wei and Lin, 2010;Vidal and Favaro, 2014) and R-PCA (Wright et al, 2009;Candès et al, 2011), showing that, surprisingly, their solutions are mutually expressible. Similarly, R-LatLRR (Zhang et al, 2014) and R-PCA are closely connected too.…”

Section: Our Contributionsmentioning

confidence: 51%

“…Rank minimization methods account for a large class of subspace clustering algorithms, where rank is connected to the dimensions of subspaces. Representative rank minimization based methods include Low Rank Representation (LRR) (Liu and Yan, 2011;Liu et al, 2013), Robust Low Rank Representation (R-LRR) (Wei and Lin, 2010;Vidal and Favaro, 2014) 1 , Latent Low Rank Representation (LatLRR) (Liu et al, 2010;Zhang et al, 2013a) 1 Note that Wei and Lin (2010) and Vidal and Favaro (2014) called R-LRR as Robust Shape Interaction (RSI) and Low Rank Subspace Clustering (LRSC), respectively. The two models are essentially the same, only differing in the optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Relations Among Some Low-Rank Subspace Recovery Models

et al. 2015

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Recovering intrinsic low-dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, a lot of work has modeled subspace recovery as low-rank minimization problems. We find that some representative models, such as robust principal component analysis (R-PCA), robust low-rank representation (R-LRR), and robust latent low-rank representation (R-LatLRR), are actually deeply connected. More specifically, we discover that once a solution to one of the models is obtained, we can obtain the solutions to other models in closed-form formulations. Since R-PCA is the simplest, our discovery makes it the center of low-rank subspace recovery models. Our work has two important implications. First, R-PCA has a solid theoretical foundation. Under certain conditions, we could find globally optimal solutions to these low-rank models at an overwhelming probability, although these models are nonconvex. Second, we can obtain significantly faster algorithms for these models by solving R-PCA first. The computation cost can be further cut by applying low-complexity randomized algorithms, for example, our novel l2,1 filtering algorithm, to R-PCA. Although for the moment the formal proof of our l2,1 filtering algorithm is not yet available, experiments verify the advantages of our algorithm over other state-of-the-art methods based on the alternating direction method.

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Section: Our Contributionsmentioning

confidence: 51%

Section: Introductionmentioning

confidence: 99%

Relations Among Some Low-Rank Subspace Recovery Models

et al. 2015

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“…To show the robustness of our technique, we first present comparisons of the proposed DLR algorithm with LRR [1] and robust shape interaction (RSI) [4] on synthetic data under the context of subspace segmentation. We construct five independent subspaces as five categories of data set; each of them has a rank of 10.…”

Section: Resultsmentioning

confidence: 99%

Robust low‐rank image representations by deep matrix decompositions

Yang

et al. 2014

Electron. lett.

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A novel approach based on low-rank representations (LRRs) for image representations is proposed. LRR seeks the lowest-rank representations among all the coefficient matrices that represent the images as linear combinations of the basis in the given dictionary. Unlike LRR methods of enforcing additional constraints on the representation and dictionary, an iterative process in which the low-rank decomposition is performed on the coefficient matrices has been developed. The rank of the representation matrices will be lower and lower with the iterations, termed as the deep low-rank (DLR) method. Extensive experiments were conducted to verify the state-of-the-art performance for classification tasks of the DRL method.

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“…NCut: Normalized ncut [47]. SIM: Clustering using shape interaction matrix [8], derived from singular value decomposition. RPCA: Robust principal component analysis [6].…”

Section: Subspace Clusteringmentioning

confidence: 99%

“…To solve this problem, many promising approaches have been developed from various perspectives, such as robust principal component analysis (RPCA) [1], sparse representation (SR) [5,6] and low-rank representation (LRR) [7]. In this work, we focus on low-rank based methods as it has found wide applications in robust recovery analysis [2], subspace segmentation [8], matrix completion [9], etc.…”

Section: Introductionmentioning

confidence: 99%

Towards robust subspace recovery via sparsity-constrained latent low-rank representation

et al. 2016

Journal of Visual Communication and Image Representation

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Spectral clustering steered low-rank representation for subspace segmentation

Cited by 16 publications

References 41 publications

Relations Among Some Low-Rank Subspace Recovery Models

Relations Among Some Low-Rank Subspace Recovery Models

Robust low‐rank image representations by deep matrix decompositions

Towards robust subspace recovery via sparsity-constrained latent low-rank representation

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